Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:244

Article

Faria, Teresa^1,2  Oliveira, Jose J.³ 

[1] Univ Lisbon, Fac Ciencias, Dept Matemat, P-1749016 Lisbon, Portugal

[2] Univ Lisbon, Fac Ciencias, CMAF, P-1749016 Lisbon, Portugal

[3] Univ Minho, Escola Ciencias, Dept Matemat, P-4710057 Braga, Portugal

关键词: Lotka-Volterra system;    delayed population model;    distributed delays;    global asymptotic stability;    local asymptotic stability;    instantaneous negative feedback;   

DOI  :  10.1016/j.jde.2007.12.005

来源: Elsevier

【 摘 要 】

This paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free